The present invention relates to a three-dimensional imaging system in general, and, more particularly, to high-resolution optical tomography where the features of interest are of a size comparable to the wavelength of the light used to illuminate the objects of interest.
A tomography device is intended to produce three-dimensional reconstructions of objects by providing a measure of light or x-ray attenuation along a set of ray paths through the object. Thus the existence of a focal plane within the object region is forbidden, i.e., the depth of field is infinite, and all the photons reaching an individual detector pixel element have, ideally, traveled along the same geometric path. For x-ray tomography, scattering from inhomogeneities within the object region is not an issue, because the size of such features is typically much larger than the wavelength of the incident radiation. In optical tomography, however, the wavelengths are much longer than they are in the case of x-ray tomography. Therefore, scattering from features within the object region can introduce noise into the system by causing several light rays to reach the same individual detector element after traveling along several different paths between the source and that detector element. The present invention exploits such scattering effects to acquire information about a three-dimensional object region, and re-arranges that information by mapping the spatial-frequency domain (k-space) into real space.
A. C. Kak and M. Slaney, in their book entitled Principles of Computerized Tomographic Imaging (IEEE Press, 1988), describe the use of the Fourier Slice Theorem to map transmitted or reflected light from the spatial domain into the frequency domain, as depicted in FIG. 1. By obtaining projection images from multiple viewpoints and applying a two-dimensional Fourier transform to each one, a set of planar surfaces through the frequency domain (k-space) can be generated. The sum of these planar surfaces can then be operated upon by a three-dimensional inverse Fourier transform to yield a three-dimensional reconstruction of the object region. In the presence of weak scattering within the object region, the planar surfaces become spherical surfaces, and the Fourier Diffraction Theorem should be substituted for the Fourier Slice Theorem. However, both of these approaches break down when strong scattering is present. The Fourier transform of a single projection maps a set of spherical surfaces through k-space, resulting in ambiguous values when the surfaces from different viewpoints are summed.
Work by Pernick, et al. (1978), Wohlers, et al. (1978), and Backman, et al. (2001) has demonstrated the usefulness of examining biological material in the two-dimensional Fourier domain. (See, for example, B. Pernick et al., xe2x80x9cScreening of cervical cytological samples using coherent optical processing. Part 1,xe2x80x9d Appl. Optics 17, 21 (1978), R. Wohlers et al., xe2x80x9cScreening of cervical cytological samples using coherent optical processing. Part 2,xe2x80x9d Appl. Optics 17, 35 (1978), B. Pernick et al., xe2x80x9cScreening of cervical cytological samples using coherent optical processing. Part 3,xe2x80x9d Appl. Optics 17, 43 (1978), B. J. Pernick et al., Paraxial analysis of light scattering by biological cells in a flow system,xe2x80x9d Appl. Optics 17, 3205 (1978), V. Backman et al., xe2x80x9cMeasuring Cellular Structure at Submicrometer Scale with Light Scattering Spectroscopy,xe2x80x9d IEEE J. Selected Topics Quantum Electron. 7, 887 (2001)).
Techniques for using light diffraction to examine small features in an object have been described by Kopp, et al. in U.S. Pat. No. 4,150,360, issued Apr. 17, 1979, entitled xe2x80x9cMethod and Apparatus for Classifying Biological Cells,xe2x80x9d and U.S. Pat. No. 4,213,036 issued Jul. 15, 1980 entitled xe2x80x9cMethod for Classifying Biological Cells.xe2x80x9d Kopp, et al. used Fourier optics to acquire a single two-dimensional Fourier transform of a biological cell. However, three-dimensional object regions were not considered by Kopp, et al. In contrast, the method and apparatus of the present invention acquires multiple two-dimensional Fourier transforms from several different viewpoints. Using the different viewpoints, a three-dimensional Fourier transform is computed using conventional image reconstruction techniques that may be modified according to the specific geometric configuration.
In contrast to known methods, the present invention provides a method that allows real-time, in-situ processing of the light passing through the entire volume of the specimen region. The method of the present invention uses Fourier optics to map the angular distribution of light exiting the object region into real space at the back focal plane of a lens or mirror system. As a result, the three-dimensionality of the object region ceases to pose a problem, since in optical tomography the light rays need not originate within a single plane.
The present invention provides a method and apparatus for multi-dimensional imaging of an object region. The method includes the step of passing collimated light through an object region to produce transmitted light rays. In another step, the transmitted light rays are captured by at least one optical element, each of said at least one optical element having a back focal plane. At least one detector is used to capture a power distribution of a two-dimensional Fourier transform, where the at least one detector is located in a back focal plane of the least one optical element. For two or more viewpoints, the steps of the method are repeated about an arc at least partially encircling the object region to obtain multiple two-dimensional Fourier transforms.